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Problem-solving and enquiry-based learning are integral in the Mathematics and Science curriculum in South Africa through online-based assessment. Online assessment has rapidly gained recognition because of technology. In this paper, the authors explored the views of online baseline assessment among Senior Phase First-year Mathematics Student Teachers. The researchers adopted a qualitative research method. Data was collected from the participants using an online Google form developed into a questionnaire. The participants in this study were first-year students enrolled for the Bachelor of Education in Mathematics at a university in a rural province of South Africa. The first-year student teachers were exposed to the senior phase baseline assessments through the licensed online Computer Aided Mathematics Instruction (CAMI) tool. One hundred and sixteen (116) senior-phase student teachers completed the online questionnaire. This study used convenience sampling since it was the most appropriate method to conveniently invite the participant. The findings revealed that first-year student teachers were enthusiastic and motivated to write the baseline assessment on computers for the first time. The result also showed that several first-year student teachers experienced difficulties solving mathematics problems using computers. This study recommends more intensive research on student teachers' views on online assessment regarding gender and time.

Background: The presence of African women in mathematics has been nearly invisible. The underrepresentation of African women in this field is a result of their historical socio-political marginalisation. The mathematics discipline is politicised, racialised, and gendered to systematically oppress African women. The mathematics fields continue to be a masculine and white male dominated field, which reinforces and preserves masculine culture which is hostile and unwelcoming to women. African women mathematicians are further oppressed because of their racial and gendered identities in fields that are ideologically founded on proving the racial, gendered, social, cultural, and intellectual inferiority of Africans. Aim: The article aims to exemplify the lived experiences of African women doctoral students in the mathematics disciplines in South African universities. The article critically interrogates the factors that influence the participation, progression, and retention of African female doctoral students in the mathematics disciplines. Setting: The article comes from a larger study which investigated the reasons why African doctorate students do not become academics after they receive their doctorates in science, technology, engineering and mathematics (STEM) disciplines in South African universities. This paper focuses on the experiences of 10 African female doctoral students at five universities in South Africa. The universities were selected because they ranked in the top five in South Africa. Two of the institutions are historically Black universities and the rest are historically white institutions, with one historically Afrikaner-speaking university--between 2019--2021. Methods: This article employed a qualitative research methodology, where semi-structures interviews were conducted with 10 African female doctoral participants in mathematics disciplines in five South African universities and is underpinned by the theory of intersectionality. Results: The findings reveal how interlocking systems of oppression continue to influence the recruitment, retention, and progression of women in the mathematics discipline, thereby providing insight into the mechanisms that need to be altered and/or put in place to actively recruit African female doctoral students and retain them in academic positions. Conclusion: The article concludes that despite the mathematics field proclaiming neutrality and objectivity nevertheless, African women still experience racism, sexism, and classism. The experiences of African women in mathematics are vital to understanding the reasons why there is a high attrition rate of African women in the mathematics discipline in academia and why they do not become academics when they could transform this discipline.

Learners' participation in mathematics decreases during their transition from primary to high school. This is despite adolescents' cognitive growth equipping them with enhanced cognitive ability; to learn mathematics. Hence low participation in mathematics does not result from cognitive deficiency. Rather, lack of motivation to learn mathematics may be the factor. According to self-determination theory, motivation results from nurturing three human basic needs: autonomy, connectedness and competence. Since identity is linked to autonomy, identities in mathematics learning impacts motivation to learn the subject. Hence, this paper reports on the action research intervention which took advantage of adolescents' preoccupation with identity formation. In line with continuous cycles of action research, the intervention is the pilot of the ongoing study that seeks to enhance mathematics learning by utilizing non-cognitive factors that resonate with the characteristics of adolescents. The paper reports on how the autonomy to form their identities in mathematics learning, impacted the adolescents' learning and attitude towards mathematics. Qualitative results show that learners lived up to their self-formed identities and this enhanced their motivation to learn mathematics. Further studies that forge positive identities in mathematics classrooms to enhance motivation to learn mathematics are recommended.

When embarking on our journey of learning in mathematics, we may envision a linear path of modules for acquiring mathematical knowledge and understanding to reach a predetermined outcome. However, this is a partial representation since the outcome and path are developing and adapting and our learning is continuously emerging. In this paper, our journey of learning in mathematics is re-envisioned as a complex adaptive system with agents, internal diversity, internal redundancy, decentralised control, sources of disruption and sources of coherence. As will be illustrated through the adaptive cycle of a complex adaptive system, learning may emerge between phases of destabilisation and development. For this emergence there needs to be openness to embrace a disruption, reflection to interpret the disruption, connection to respond to the disruption and inspiration to grow and adapt in response to the disruption. There also needs to be a balance between individual and collective learning. Through navigating these cycles along our journey of learning there may be emergence of learning experiences within and beyond mathematics.

Pre-service secondary mathematics teachers have a poor command of the exact language of mathematics as evidenced in assignments, micro-lessons and practicums. The unrelenting notorious annual South African National Senior Certificate outcomes in mathematics and the recognition by the Department of Basic Education (DBE) that the correct use of mathematical language in classrooms is problematic is reported in the National Senior Certificate Diagnostic Reports on learner performance (DBE, 2008-2013). The reports further recognise that learners do not engage successfully with mathematical problems that require conceptual understanding. This paper therefore highlights a need for teachers to be taught and master an exact mathematical language that for example, calls an "expression" an "expression" and not an "equation". It must support the call of the DBE to use correct mathematical language that will support and improve conceptual understanding rather than perpetuate rote procedural skills, which are often devoid of thought and reason. The authentic language of mathematics can initiate and promote meaningful mathematical dialogue. Initial teacher education programmes, as in the subject methodologies, affords lecturers this opportunity. The language notions of Vygotskian thought and language, Freirian emancipatory critical consciousness and Habermasian ethical and moral communicative action frame the paper theoretically. Using a grounded approach, after examining examples of student language in a practice based research intervention, the design and development of a repertoire of language categories, literal, algebraic, graphical (Cartesian) and procedural (algorithmic) emerged from three one-year cycles of an action research methodology. The development of these repertoires of language was to assist teachers in communicating about mathematical objects through providing a structured framework within which to think and teach. A course model encompassing small group discussions, an oral examination and a self-study action research project, that helped sustain the teaching of an exact mathematical language, is presented. This is supported by student reflections on the usefulness of implementing them.

This paper reports on the findings of a baseline study that fed on to a broader investigation exploring ICT integration in the teaching of functions. The baseline study was premised on the observation that the notion of function, despite being a fundamental and central idea in the mathematics school curriculum, presents pedagogical challenges to both teachers and learners. The study used the qualitative case study design to investigate Grade 11 mathematics learners' errors and misconceptions under hyperbolic functions at a rural high school in the Limpopo province of South Africa. Informed by the constructivist APOS theory conception levels, learners' errors were detected from their written responses in a diagnostic test. The learners were then individually interviewed during task-based interviews to infer on the misconceptions underlying their errors. Qualitative analysis of the data revealed the following categories of misconceptions: algebraic, conceptual, asymptotic, graphical, and notational misconceptions. The study established that errors, if diagnosed and corrected, are springboards and milestones to the formulation and construction of proper mathematical ideas. To resolve learners' misconceptions, this study recommends that teachers should use explorative and discovery pedagogical strategies to enable learners realize their own misconceptions and self-correct. Based on the findings of this study, the integration of Information and Communication Technologies (ICTs) in teaching functions as an intervention strategy will be explored.

In this paper, I argue that the establishment of after-school mathematics clubs in early grades holds rich potential for supporting the development of increasingly participatory and sensemaking maths learning dispositions. Within the South African Numeracy Chair project, lead by the author, multiple after-school mathematics clubs have been set up for learners in Grades 3-6 across Eastern Cape schools. These clubs are a complementary initiative to teacher development, aimed at improving low levels of numeracy learning across the majority of schools in the province. Two sources of data, learner interviews and teacher questionnaires, from one case study club, are shared in this article to illuminate the potential such clubs hold in developing increasingly participatory mathematics learning dispositions.

The majority of children in mainstream (no fee, poorly resourced, African language dominant) public schools in South Africa fall significantly behind curricular norms in mathematics by Grade 3; the early learning gap grows across time. The provision of quality instructional materials is a well-recognised component of effective strategies to improve early grade mathematics in low- and middle-income contexts. However, there has been little explication of what constitutes quality instructional materials, nor long-term design work to contribute theory to this instructional design challenge. Across 15 years, the author has been working in an education design hub with teacher educators and teachers in the rural Eastern Cape, with the goal of improving early grade mathematics. The gains in mathematics performance have been among the most significant reported in research literature. This paper presents the design principles emerging from the work. Engaging the theoretical layers discussed by diSessa and Cobb, the paper contributes to design theory by emphasising the relationship between explicit instructional assumptions and design principles, integrating four ontological categories (motive, pedagogy, language use and mathematical meaning-making). Since 2011, the Department of Basic Education has provided learner workbooks to support teaching and learning in foundation phase mathematics at system scale. It is hoped that this paper will contribute to the ongoing development of this vital national resource. The paper makes explicit instructional assumptions and design principles (available for critique, adaptation, and refinement), and provides a more nuanced framework through which to assess and improve materials across time. [ABSTRACT FROM AUTHOR]

This paper analyses student teachers' meta-narratives associated with 'doing' mathematics. The quality of the vocabulary associated with the doing of the mathematical objects of a sample of 56 multilingual third-year mathematics methodology students preparing to be secondary teachers was explored and assessed. Sfard's theoretical concept of 'pronounced foci' and her 'critical categories' for determining if a narrative was mathematical were used to analyse the data. Meta-narratives refer to the written mathematical metacognitive monologues that manifested students' thinking while they were doing the mathematical objects. Students were required to write, in language suitable for teaching, a description of the procedure which led to a solution. The procedures and their associated meta-narratives provided data for a mixed-method analysis in this case study. The absence of a mathematical vocabulary presented difficulties when students engaged in meta-narratives. The data also show that inexact mathematical vocabularies are not culturally specific since the 11 English mother tongue students demonstrated a similar lack of command of mathematical language as their peers. Meta-narratives revealed mathematical misconceptions that may not have been detected without them. For two of the three mathematical objects there is a significant but moderate positive correlation between correct vocabulary and correct procedure. The findings support the need for mathematical vocabulary (and language) to be a teaching focus when preparing teachers for their careers and that the assessment of tasks is not completely achieved by evaluating only the procedural 'doing' of mathematics.

One challenge for an optimal design of the mathematical components in engineering education curricula is to understand how the procedural and conceptual dimensions of mathematical work can be matched with different demands and contexts from the education and practice of engineers. The focus in this paper is on how engineering students respond to the conceptual-procedural distinction, comparing performance and confidence between second and fourth year groups of students in their answers to a questionnaire comprising conceptually and procedurally focused mathematics problems. We also compare these students' conceptions on the role of conceptual and procedural mathematics problems within and outside their mathematics studies. Our data suggest that when mathematical knowledge is being recontextualised to engineering subjects or engineering design, a conceptual approach to mathematics is more essential than a procedural approach; working within the mathematical domain, however, the procedural aspects of mathematics are as essential as the conceptual aspects.

This paper presents an enrichment case study to showcase a possible avenue for attending to the needs of academically strong mathematics students. We report on a group of university students who were presented with the opportunity of exploring a specific first year mathematics topic deeper, using an inquiry-based learning approach as part of an enrichment programme. Following the intervention, students completed a questionnaire and a few were interviewed to establish their experiences of the enrichment programme. We discuss the successes and pitfalls of the intervention and report on the impact it had on the participants.

This study focuses on the mathematics department at a South African university and in particular on teaching of calculus to first year engineering students. The paper reports on a cause-effect analysis, often used for business improvement. The cause-effect analysis indicates that there are many factors that impact on secondary school teaching of mathematics, factors that the tertiary sector has no control over. The analysis also indicates the undesirable issues that are at the root of impeding success in the calculus module. Most important is that students are not encouraged to become independent thinkers from an early age. This triggers problems in follow-up courses where students are expected to have learned to deal with the work load and understanding of certain concepts. A new model was designed to lessen the impact of these undesirable issues.

The research interest underpinning this paper concerns the type of mathematical knowledge engineering students may acquire during their specialised education in terms of the conceptual and procedural dimensions of doing and using mathematics. This study draws on interviews with 25 qualified engineers from South Africa and Sweden regarding their views on the role of mathematics in engineering education, with special focus on the conceptual and procedural aspects of mathematical knowledge. A thematic analysis of the interview data led to the identification of two main themes. According to the conceptual view a predominantly conceptual approach is needed and valued more than procedural skills, while the balanced view emphasises a balance of conceptual understanding and procedural fluency as well as links between them. It is suggested that the mathematical education of engineers would need to be more conceptually oriented to prepare for the demands at the workplace.

This article discusses the growing attention and research activity surrounding early grade mathematics (EGM) in South Africa and Malawi. The introduction of curriculum reforms and policy-linked interventions, such as the Teaching Mathematics for Understanding model and the Primary Teacher Education initiative, have led to increased research in this field. The article highlights the importance of foundational understandings of mathematics in addressing low performance in the subject. It also examines different approaches to EGM research, including large-scale interventions and projects that engage with the mathematics education literature base. The article concludes by emphasizing the need for ongoing attention to both larger-scale and smaller-scale intervention studies in order to improve mathematical outcomes. [Extracted from the article]

"Personal learning environments" (PLEs) and "personal learning networks" (PLNs) are well-known concepts. A personal learning network "cluster" is a small group of people who regularly interact academically and whose PLNs have a non-empty intersection that includes all the other members. At university level PLN clusters form spontaneously among students and are known to last over an extended period of time. Little is known regarding the workings of these PLN clusters of students. The claim is that these PLN clusters are at the heart of student learning and are aligned with the current trend of a knowledge-pull community of learning. In this paper we investigate the activities and characteristics of PLN clusters in two different fields of study at a South African university, namely mathematics and computer science. We discuss the benefits that these clusters offer, investigate the mashup of activities and tools and we contrast experiences in the two fields of study. It is the commonalities rather than differences that are striking between the two groups of students. Although computer science students lean more towards digital communication, both groups impress with the pride they take in their PLN clusters and are vocal in describing the benefits that these clusters offer.

Teacher quality in primary schools in South Africa is a serious concern, and how best to prepare teachers in initial teacher education—with regard to mathematics—remains an open and vexing question. There is a confluence of challenges facing the mathematics education community in South Africa: poor conceptual understanding of mathematics amongst teachers; poor attainment in Primary Teacher Education mathematics tests at both first and fourth year levels; and few initial teacher education programmes having evidence of improving knowledge for teaching mathematics. In addition, few lecturers in initial teacher education make explicit the theoretical tenets informing their course design for mathematics. In response to the latter challenge, this paper makes explicit the design choices made in the Emergent Number Sense first year mathematics module in Bachelor of Education degrees, used across six universities in South Africa. It then theorises the choice to commence the B.Ed mathematics programmes with two pathways into number knowledge: (1) a counting pathway, making use of discrete objects or events which can be quantified by counting in ones; and (2) a measurement pathway, making use of continuous extents which can be quantified by introducing a unit of measurement. Each has a distinct metaphor, strategy for the reification of the 10 and supporting representation. This offers the lecturers using the course in their own design trials, and initial teacher educators beyond the Maths4Primary Teachers collective, a conceptual framework for this design choice, which can now be critiqued and further improved. [ABSTRACT FROM AUTHOR]

Research on mathematical equivalence, and to some extent, on number structure in early grade mathematics, has shown that most students at primary and secondary levels understand these concepts instrumentally rather than relationally. The study reported in this paper uses a design research approach to explore both mathematical equivalence and number structure in a primary pre-service teacher education programme at a university in South Africa and reports on an intervention strategy intended to culminate in developing design principles comprising guidelines for the effective teaching of number structure and mathematics equivalence in primary pre-service teacher education programmes. The mixed method study comprises 70 first-year primary pre-service teachers (PSTs) and a teacher educator. The PSTs wrote pre- and post-tests, and were interviewed following the pre-test. Skemp's notion of relational and instrumental understanding guided the design of the intervention and the analysis of the data. The results from the study indicates that PSTs' understanding of the notion of equivalence is similar to what has been reported for students in schools, and that there were some learning gains in the post-test results. Based on the findings from the study in general, some emergent design principles are proposed. [ABSTRACT FROM AUTHOR]

In South Africa, there is no adequate research that explored mathematics learning and teaching within rural schools and classrooms. Various literature posits that mathematics education research has virtually over-concentrated on urban and township schools and consistently ignored rural contexts and schools. Arguments exist that rural education and rural education research have been understudied in South Africa. Presumably, this would include mathematics education research as well. This paper explores the relationship between witchcraft beliefs, which is considered as an entrenched cultural phenomenon, and learners' mathematics learning within rural classrooms. In this paper, the local influences include that the learners end up not demonstrating their full understanding of mathematics contents because of the beliefs that if they exhibit their knowledge of the subject, they may be bewitched. Cultural Relativism was used to theorise the study within qualitative critical phenomenology as a methodology for the study. The study comprises 12 mathematics learners from a rural Acornhoek region in Mpumalanga Province, and data were collected using individual semi-structured interviews while the collected data were analysed using Critical Discourse Analysis. Findings from this study illuminated that local beliefs and knowledge such as witchcraft exert significant influence on schools and learners' learning, including learners' not demonstrating their optimum understanding of mathematics. [ABSTRACT FROM AUTHOR]

Given the importance of mathematics performance of learners and the challenges in South Africa, it is important that the expertise of all role-players, including the subject advisors who visit the teachers to guide and support them, is used to its full potential. While some studies have explored the experiences of teachers in this regard, literature on the experiences of mathematics subject advisors is scant. Furthermore, little has been published on the experiences of subject advisors within the context of rural areas with a low population, such as the Northern Cape Province. This article addresses the gap by exploring the deeper understanding of mathematics subject advisors’ experiences when conducting school support visits. Taking a qualitative research approach, I conducted semi-structured interviews with six mathematics subject advisors from the four phases (foundation, intermediate, senior, and further education and training) in all five of the education districts of the Northern Cape Department of Education (Frances Baard; Z.F. Mgcwawu; Pixley Ka Seme; Namakwa; and J.T. Gaetsewe). Through Husserl’s phenomenological theoretical framework, complemented with Gibbs’ reflective cycle and Colaizzi’s seven steps of data analysis, participants were found to have had both good and bad experiences when conducting school support visits. Experiences included positive attitudes from educators and schools in general, and good curriculum implementation and teaching and learning practices. However, participants were sometimes received with hostility, and observed poor curriculum implementation and teaching and learning practices. Noteworthy is some negative union influence, lack of specialisation in mathematics by foundation phase departmental heads, lack of coherence in communication, and lack of cooperation and collaboration amongst district officials. If the concerns raised by mathematics subject advisors in this paper are not addressed, these may have a negative impact on the experiences of subject advisors and, by implication, on learner performance as well as education in general. [ABSTRACT FROM AUTHOR]

Mathematics is a core subject in South Africa. Studies have shown that the performance of learners on this subject is not encouraging. Many factors have been alluded to by scholars as contributing factors to this poor performance. The gap between theory and practice of mathematics teaching can be bridged by the use of appropriate learning styles, availability, and utilization of instructional. This paper finds out the relationship that exists among learning styles, instructional materials, and mathematics performance of Grade 6. The choice of Grade 6 is important because it is the last grade level of primary school before a learner can enter secondary school level in South Africa. The study adopted a correlational research design of a quantitative approach. Stratified sampling techniques were used to select 1225 learners from Grade 6 schools within Buffalo City Metropolitan Education District. The data revealed among others that in Buffalo City, availability and utilization of instructional materials have no significant relationship with the mathematics performance of selected grade 6 learners (B=.023, t=.804, P=0.05) while students learning styles (visual, auditory, and kinesthetic) have a significant relationship with grade 6 learners Mathematics performance (B=-.113, t=-3.886, p<0.05). The study concluded that one of the most fundamental issues to consider in improving Mathematics performance is the understanding of the learners' learning styles and effective use of appropriate instructional materials for teaching Mathematics. [ABSTRACT FROM AUTHOR]

TB is rated as one of the world’s deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014. [ABSTRACT FROM AUTHOR]

This paper examines whether tobacco expenditure leads to the crowding out or crowding in of different expenditure items in South Africa. We apply genetic matching to expenditure quartiles of the 2010/2011 South African Income and Expenditure Survey. Genetic matching is a more appealing approach for dealing with the endogeneity of tobacco expenditure that often plagues studies using systems of demand equations. Further, genetic matching provides transparent measures of covariate balance giving the analyst objective means of assessing match success. We find that the poorest tobacco consuming households in South Africa consistently allocate smaller budget shares towards food items than non-smoking households. Specifically, we find that dairy, fruits, nuts and oils are displaced in favour of tobacco expenditure in the two poorest quartiles. Unsurprisingly, food items are never displaced for households in the top two quartiles, given these households’ greater access to resources. Like other studies in the literature, we find that tobacco expenditure consistently crowds-in alcohol across all quartiles confirming the strong complementarities between the two. [ABSTRACT FROM AUTHOR]

There is concern over the learning and teaching of mathematics in South Africa. The aim of this study was to explore high school mathematics teachers' conceptual difficulties in trigonometry and coordinate geometry. The participants were in-service teachers (n = 236), who were enrolled in an in-service programme at a South African university. The research instrument was based on a previous Grade 12 national mathematics paper. The study used Duval's theory on semiotic systems to try to understand the teachers' difficulties experienced with the content. Ethical clearance was obtained from the university research office for the collection of data. All participants provided informed consent to participate in the study. The study used a mixed methods approach where the quantitative data was first analysed. Thereafter a content analysis was conducted on 50 scripts to gain insight into the areas which presented challenges to the teachers. The results showed that the teachers obtained an average of 55% overall in the items. The average for the trigonometry and coordinate geometry was 52% and 61% respectively. The study suggests that teachers need more support in mastering the Grade 12 content and developing representational fluency. [ABSTRACT FROM AUTHOR]

This paper focuses, empirically, on the developments seen in a group of South African early grades' mathematics teacher educators in the course of a university-provincial education department partnership project. This project sought to support the district Mathematics Subject Advisers to support, in turn, teachers to implement an intervention consisting of a sequence of four lessons focused on multiplicative reasoning. Outcomes based on pre- and post-tests administered by the Subject Advisers suggested substantial pre- to post-test improvement at the student level. Subject Adviser observations and reflections pointed to successes in engendering more dialogic conversations between mathematics teachers and mathematics teacher educators focused on mathematics and its teaching and learning. The 'double move' of increasing overlap between the subject adviser and teacher communities, coupled with evidence that implementing the intervention had enabled the Subject Advisers to develop their mathematical and pedagogical understandings, provides a useful way of considering development in the capacity of mathematics teacher educators to support mathematics teaching and learning. [ABSTRACT FROM AUTHOR]

Since 2016, all the second-year Intermediate Phase students at the University of the Free State (UFS), South Africa, who have enrolled for the MTBI2503 module have been exposed to family math (FM) activities during six compulsory contact sessions. The main aim of the FM training sessions for student-teachers was to expose them to reallife and hands-on mathematics teaching and learning. It was decided by the key role players that the FM program should be subjected to formative evaluation. A self-constructed questionnaire was used as an assessment tool. The first section of the questionnaire focuses on the generics of the program (FM training program per se, content, training outcomes, course material, and assessment). This paper reports on data from the second section of the questionnaire and aims to answer the following research question: Are MTBI2503 students satisfied with the way the UFS adapted the FM program to make provision for Intermediate Phase students' specific expectations and needs? Statements relating to the FM program are evaluated using five-point Likert scale items. Overall, the rating of the contact sessions, teaching and learning, facilitators, and personal experiences of the students are high. It was concluded that an awareness of the inherent educational value of the FM program for Intermediate Phase students may have a positive influence on future initial teacher training programs in South Africa. [ABSTRACT FROM AUTHOR]

This paper is centred around a framework for studying teaching—Mediating Primary Mathematics (MPM)—developed in the context of the teaching of Whole Number Arithmetic (WNA) in South Africa. Findings from the analysis of four WNA lessons are used to illustrate how the application of the MPM framework can measure nuanced differences in the meditational means—both artefact- and human-based—employed by teachers. Detailed analysis of differences observed across these lessons shows that the mathematics taught can go beyond localized procedures and counting-based methods, and engage learners in mathematical activity that involves affordances for making connection and generalizing, particularly with respect to counting with composite units, a key developmental stage in WNA. [ABSTRACT FROM AUTHOR]

This paper considers the effects of both free optional mathematics learning support and engagement on the mathematics performance in a foundation mathematics subject of a cohort of engineering students entering university with poor mathematical skills. New engineering students were directed to either a foundation or standard mathematics subject based on the results of a placement test. For students in the foundation subject, it was found that high levels of learning support were associated with greater improvement over the semester. Some form of learning support was used by 57.9% of the students, a reasonably high proportion of the cohort. Some factors for this high level of use of learning support are considered. One possible factor, the placement test, appears to have had a positive effect. Engagement in the subject activities as measured by tutorial attendance and learning management system use was found to have a positive association with final mark. Students who utilized a high level of learning support were more likely to be more engaged with the subject, making it impossible to draw conclusions about improvements being solely due to the use of learning support. [ABSTRACT FROM AUTHOR]

Although buoyed by the induction of a democratic government, and the high ideals of our constitution, the South African education system has in many ways not met the expectations of its people, in this case, the mathematics education community. With the birth of an expansive intended curriculum came the monitoring of the outcomes through systemic type testing, the so-called attained curriculum. In time, it became clear that the inevitable 'teaching to the test' would constitute a narrowing of the implemented curriculum. Two possible constraining influences of the systemic test were identified, namely, a narrowing of the curriculum, and reliance on only one source of external monitoring. To counteract these, a project titled Assessment Enhanced Teaching and Learning (AETL) has been initiated, involving Grade Nine mathematics teachers. The aim of the project is to provide intermittent markers of progress to the teachers and learners at strategic points throughout the year. Teacher involvement in the design and implementation of these formative assessment tasks is thus central to the project. In this paper, we report on a case study at one school in the Pretoria region, and explore the use of structured assessment tasks as an approach to professional development. The question posed here is, "How does the implementation of strategically designed assessment tasks support professional development and enable professional agency?" Our findings indicate a strong sense of agency motivated by the need to excel in systemic type testing. [ABSTRACT FROM AUTHOR]

The study reported on here was conducted to explore four Grade 7 mathematics teachers' understanding of the relationship between the objectives indicated in the CAPS for teaching different topics/concepts and instructional time stipulated for doing so. Seven lessons were studied in 4 primary schools in the Vhembe district of the Limpopo province, South Africa. A constructivist philosophical approach was used. The data collection methods included interviews and classroom observations. The main finding indicates teachers' understanding of instructional time as either a regulatory or a teaching tool. The ability to translate instructional time into social time depends on the level of teachers' curriculum literacy. Consideration of how CAPS objectives could be fulfilled based on the topic/concept to be taught and the stipulated instructional time, influenced the learners' conceptual understanding, procedural fluency, and competency in mathematics. The conclusion underscores the importance of instructional time as both an essential authoritative regulatory tool and signal of a pedagogic device and communication required to advance the instructional objectives. [ABSTRACT FROM AUTHOR]

Participating in classroom mathematics conversations, particularly engaging with the opinions of others, can improve learners' mathematical comprehension. Teachers can use a variety of invitation and follow-up moves to encourage student engagement. The study aimed to explore teacher follow-up on learners' initial responses to teacher questions and building on learner ideas in Grade 9 mathematics classrooms. A qualitative approach and descriptive case study design were utilised. Data were collected from three schools in the same circuit in South Africa through classroom lesson observations, face-to-face teacher interviews and researchers' field notes. Three Grade 9 mathematics teachers, one from each school, were purposively selected, and the selected teachers' already established Grade 9 classes, with a maximum of 30 learners each (owing to the COVID-19 health protocol), were automatically involved. Cognitively guided instruction, a learner-centred approach that uses social constructivism as a research paradigm, guided this study. The exploration was supplemented by Brodie's conceptual framework on teacher follow-up moves. The findings revealed that the three teachers followed up on learner contributions and used different follow-up moves, namely insert, elicit, press, maintain and confirm. The study showed hybrid teacher moves. Although more teacher moves were skewed towards elicit and insert, which are closer to traditional practices, there is an indication of moving towards the press, maintain and confirm, which are reform-oriented moves. In addition to these moves identified by Brodie, acknowledging or praising the learner for responding was another move that emerged in this study. [ABSTRACT FROM AUTHOR]

This paper reports the findings of an evaluative study of an initiative, in its sixth year of implementation, enhancing the learning and teaching of mathematics in 20 disadvantaged secondary schools in KwaZulu-Natal (KZN), South Africa, twenty years after democracy. Findings highlight the importance of initial and ongoing professional development for under-qualified teachers. Support and strategies that have enhanced the achievement in mathematics of learners in these still underresourced schools, are described. [ABSTRACT FROM AUTHOR]

The aim of this paper is to discuss the barriers that learners encounter when learning mathematics and to explore an approach that will simplify the teaching of mathematics in Foundation Phase. A qualitative research design within the interpretive paradigm was used. Five professionally qualified Grade 3 mathematics teachers were sampled from five primary schools in the Tshwane South District in South Africa. The data was collected through lesson observation, interviews and focus groups. The data was analysed by reading transcripts to identify patterns that emerged from the data; these patterns were developed into categories. The participants in this study included Grade 3 mathematics learners. Grade 3 learners were selected because they have already done all the mathematics computations. The research revealed that the main barriers to understanding mathematics relate to language, an inability to solve word sums, being unable to carry over to the tens/hundreds, and confusing multiple signs and addition signs. Recommendations were that the teachers should not handle too many aspects at any given time. Until the teachers are sure that the learners have mastered one element or function, such as addition, they should not move to the next section. [ABSTRACT FROM AUTHOR]

The unsatisfactory mathematics performance of South African learners has long been a concern. South Africa is ranked among the lowest performing countries in mathematics, calling for a rethinking of the way the subject is being taught. Mathematics needs to be contextually relevant and interesting for learners to be motivated to learn. Ethnomathematical games provide a means of making mathematics meaningful to learners because of the potential mathematical knowledge embedded in them. Playing gamesis a fun way of learning, and indigenous games are an integral part of learner culture. The aim of this article is to explore the games played by community elders to determine how the games can be used in the classroom. We employed observations and interviews to collect data from community elders on the indigenous games. This article is framed by the following research question: which indigenous games, with mathematical relevance are played by community elders, and what mathematical skills and knowledge are identifiable in the games? The study offers four (4) main findings that are relevant to address the crisis in mathematics teaching and learning. Thisstudy identified various ethnomathematical games and various mathematical operations embedded in them. Based on these findings, recommendations are made to use ethnomathematics to improve the mathematics performance of learners in the intermediate phase. A further recommendation is that mathematics teachers need to be trained in alternate methods of mathematics instruction such as the use of indigenous games. Future research comprises the piloting of indigenous games in intermediate phase mathematics classrooms. [ABSTRACT FROM AUTHOR]

Learners are often tasked with activities that require them to solve problems in mathematics classrooms. Problem posing is one of the teaching strategies that can enable learners to appreciate the mathematics concepts to be extracted from familiar or everyday situations. However, problem posing, as a teaching and learning strategy, is mostly under-utilised, despite its potential to enhance mathematics learning. This article explores how Grade 11 learners pose Mathematics and Mathematical Literacy questions from a 2010 FIFA World Cup soccer match and determines the extent to which the questions posed by learners mirror the given soccer context. The study involved 42 participants, comprising 22 Mathematics and 20 Mathematical Literacy learners from a high school in the Soshanguve township in Tshwane, South Africa. Participants were selected through purposive sampling. Data were collected through a written task in which learners were given a scenario in the form of an extract from a 2010 FIFA World Cup soccer match report. The qualitative findings of the study show that learners were generally capable of posing or formulating questions based on the real-life soccer context provided. The analysis showed that (a) Mathematics learners formulated more questions with more mathematical terms in them than Mathematical Literacy learners did, and (b) Mathematical Literacy learners formulated questions that were more aligned to the analysis of the game than was the case with Mathematics learners. We argue that learners' responses to the task were consistent with how they were socialised with the Mathematics and Mathematical Literacy discourse. [ABSTRACT FROM AUTHOR]

This study investigated how high school mathematics teachers in South Africa integrate GeoGebra, a free dynamic mathematics software program, into their teaching practices. The research explored teachers' perceptions of the training they received for the GeoGebra software, their ability to create and implement GeoGebra-based lessons, and their confidence in using it in the classroom. The study employed an interpretive research paradigm to gather insights through unstructured interviews with four purposefully selected teachers from South Africa's Northwest Province. Despite the absence of a structured training program, the study findings indicate teachers' enthusiasm for adopting GeoGebra. The study underscores the need for the Department of Basic Education to enhance support to address potential obstacles and the importance of aligning GeoGebra training with existing guidelines for integrating information and communication technologies within the Department of Basic Education and school management. In summary, this study provides valuable insights into how professional development impacts high school mathematics teachers' incorporation of GeoGebra, with implications for the design and implementation of future programs aimed at helping teachers integrate technology into their instructional practices. [ABSTRACT FROM AUTHOR]

The introduction of progression policy, which prohibits the repetition of a grade to more than once within each of the four phases of Basic Education, was enforced in South Africa in the Further Education and Training phase in 2013, but appropriate strategies which could be applied to support progressed learners are not addressed. This research was qualitative by nature and approached according to the interpretative paradigm. It was a comparative case study, which investigated strategies to support Grade 12 progressed Mathematics learners using Information Communication Technologies in comparison with other strategies that do not apply ICT instructional technologies. Data collection strategies were semi-structured interviews, questionnaires and support policies. The study population was sixteen FET Mathematics educators from five schools in Ekurhuleni North district. The findings indicated that connectivism, when incorporated into teaching and learning, becomes an effective support tool for progressed learners. ICTs within networks makes teaching and learning more learner centred, improves participation, learner attainment and pass rate. Learners are able to learn at their own pace, in their most convenient set-up and they manage what they learn, how they learn, with whom they learn and what information they require. The study found that there are greater benefits of using ICT instructional technologies in a connectivist classroom to support progressed learners, but that traditional support strategies cannot be ruled out due to the socio-economic challenges schools under research experienced. The findings further indicated that there is a dire need of a comprehensive support policies, strategies and guidelines to support progressed and low-ability learners in Mathematics both digitally and non-digitally. [ABSTRACT FROM AUTHOR]

There is a significant body of research that indicates that the use of tablets to learn mathematics in elementary school motivates students to learn. Low mathematical attainment in international benchmarking tests of mathematics in South Africa led the authors to investigate the potential that the mobility of the tablet provided for children to learn how to reason using what Mercer called 'exploratory' talk, a form of dialogical interaction indicative of reasoning. In this article the authors investigate two grade 6 classrooms in two schools where students are learning mathematics using tablets. In this multiple case study, the authors videotaped children during mathematics lessons where they used tablets to solve mathematical problems, and the data were transcribed. Findings indicate that the tablets across both contexts facilitate what Mercer calls exploratory talk, which is indicative of reasoning and, therefore, learning. [ABSTRACT FROM AUTHOR]

Girls performing well in mathematics at school do not necessarily enrol for mathematics courses at South African universities. Teachers could be transferring beliefs about the nature of mathematics favouring boys. This paper compared male and female pre-service teachers’ beliefs about the nature of mathematics. A quantitative, descriptive research approach was adopted. One hundred and twenty-six mathematics pre-service teachers, enrolled for an undergraduate teaching training programme at a South African university, completed a questionnaire. While both genders hold the same Platonist and instrumentalist beliefs, females embrace lower experimentalist beliefs than males. Research on differences between male and female pre-service teachers’ beliefs about the nature of mathematics could promote gender equity in mathematics teacher training and better facilitation of the subject, which might consequently encourage more girls to opt for mathematics-related careers. [ABSTRACT FROM AUTHOR]

Introduction: The aim of the present study was to explore the relationship between satisfaction with life and mathematics achievement among a nationally representative sample of Grade 9 learners in South Africa. Methods: Using the Trends in Mathematics and Science Study (TIMSS 2019) based on a sample of 20,829 learners (females = 11,067 and males = 9,719), and employing structural equation modelling (SEM), we examined the nature of the relationship between satisfaction with life and mathematics achievement, considering the role of gender, parental involvement, and instructional clarity. Results: Our findings showed that satisfaction with life is positively related to mathematics achievement, but is not moderated by gender. Additionally, instructional clarity contributes to, and is a partial mediator of, the relationship between life satisfaction and mathematics achievement. This suggests that greater instructional clarity is positively associated with high achievement in mathematics, over and above the relationship with satisfaction with life. By contrast, parental involvement negatively mediates this relationship, suggesting that mathematics achievement is negatively associated with certain forms of parental involvement, such as setting time aside for homework; and checking if homework is done. Discussion: Given the tested linear relationship between life satisfaction, instructional clarity and mathematics achievement, the results of the study suggest that if wellbeing is improved and existing instructional practices are constantly reviewed, mathematics scores could be positively affected. In addition, the emerging finding on the negative role of parental involvement in the hypothesised mediated relationship suggests that learners could benefit from properly tailored, and governmentsponsored, afterschool tutoring. [ABSTRACT FROM AUTHOR]

Universal health coverage (UHC) aims to ensure people have access to the health services they need. Sixteen tracer indicators were developed for implementation by countries to measure UHC in the health system. South Africa uses 15 of the proposed 16 indicators. Operational managers in the public health care sector collect data and report on these indicators at a primary health clinic level. This qualitative study explored the knowledge and attitudes of managers toward data and UHC service indicators in a sub-district in Ugu, KwaZulu-Natal, South Africa. Operational managers saw data collection as information gathering, measuring performance and driving action. They understood UHC indicators as 'health for all' linking them to National Department of Health Strategic plans and saw the value of indicators for health promotion. They found the lack of training, inadequate numeracy skills, requests for data from multiple spheres of government and the indicator targets that they had to reach as challenging and untenable. While operational managers made the link between data, measuring performance and action, the limited training, skills gaps and pressures from higher levels of government may impede their ability to use data for local level planning and decision making. [ABSTRACT FROM AUTHOR]

South Africa exhibits one of the largest pro-girl gaps in education, yet the reasons behind this gap are poorly understood. This paper analyses South Africa's pro-girl gap in Grade 4 reading and Grade 5 mathematics achievement. I make use of Oaxaca-Blinder decomposition analysis to decompose the observed gender gaps into their explained and unexplained components, separately by school socio-economic quintile. This approach allows me to present new evidence that part of the country's pro-girl gaps in reading and mathematics are due to girls progressing through the early grades faster than boys. I also find that South African girls score higher on the constructs aimed at tapping student attitudes toward reading (reading self-efficacy and enjoyment, and engagement in reading lessons), and that these differences contribute significantly to the pro-girl gap in PIRLS reading achievement. Interestingly, despite outperforming boys in the TIMSS mathematics assessment, South African girls do not display more positive attitudes toward mathematics. The results suggest much more needs to be done to understand the reasons behind boys' disadvantage in the early grades, since much of the pro-girl achievement gap in Grade 4 reading and Grade 5 mathematics can be attributed the pro-girl advantage in grade completion in earlier grades. • South African girls outperform boys in both PIRLS and TIMSS. • This is partly due to girls progressing faster through the early grades. • Girls also display more positive attitudes toward reading than boys. [ABSTRACT FROM AUTHOR]

Background: The emergence of drug resistance among pathogens has resulted in renewed interest in bioprospecting for natural microbial products. Methods: This study aimed to bioprospecting endophytic actinobacterium associated with Aloe ferox Mill for its antibacterial activity. Endophytic actinomycetes were isolated from the gel of A. ferox Mill by surface sterilization technique using actinomycete isolation agar. The isolate with a promising antibacterial activity was identified using 16S rRNA sequence analysis. The minimum inhibitory concentration (MIC) of the extract was assessed by the micro-dilution method and its effect on the respiratory chain dehydrogenase (RCD) activity was ascertained by the iodonitrotetrazolium chloride (INT) assay. Fourier transform-infrared spectrophotometer (FTIR) and gas chromatography-mass spectrophotometry (GC-MS) were employed to identify functional groups and the chemical constituents, respectively. Results: The actinobacterium was found to be Streptomyces olivaceus CP016795.1. Its extract displayed noteworthy antibacterial activity (MIC ≤1 mg/mL) against Staphylococcus aureus (ATCC 25925), Bacillus cereus (ATCC 10102), and Escherichia coli (ATCC 25922); and showed an inhibitory effect on the RCD activity. FTIR spectrum displayed hydroxyl, amine, and aromatic groups, and the GC–MS revealed 5-Hydroxymethylfurfural as the main constituent (19.47%). Conclusions: S. olivaceus CP016795.1 can serve as a potential source of effective antibacterial compounds. [ABSTRACT FROM AUTHOR]

The aim of this study is to predict the COVID-19 infection fifth wave in South Africa using the Gaussian mixture model for the available data of the early four waves for March 18, 2020-April 13, 2022. The quantification data is considered, and the time unit is used in days. We give the modeling of COVID-19 in South Africa and predict the future fifth wave in the country. Initially, we use the Gaussian mixture model to characterize the coronavirus infection to fit the early reported cases of four waves and then to predict the future wave. Actual data and the statistical analysis using the Gaussian mixture model are performed which give close agreement with each other, and one can able to predict the future wave. After that, we fit and predict the fifth wave in the country and it is predicted to be started in the last week of May 2022 and end in the last week of September 2022. It is predicted that the peak may occur on the third week of July 2022 with a high number of 19383 cases. The prediction of the fifth wave can be useful for the health authorities in order to prepare themselves for medical setup and other necessary measures. Further, we use the result obtained from the Gaussian mixture model in the new model formulated in terms of differential equations. The differential equations model is simulated for various values of the model parameters in order to determine the disease's possible eliminations. [ABSTRACT FROM AUTHOR]

This study quantifies a year's worth of mathematics learning in South Africa (0.3 standard deviations) and uses this measure to develop empirically calibrated learning trajectories. Two main findings are (1) only the top 16% of South African Grade 3 children are performing at an appropriate Grade 3 level. (2) The learning gap between the poorest 60% of students and the wealthiest 20% of students is approximately three Grade-levels in Grade 3, growing to four Grade-levels by Grade 9. The paper concludes by arguing that the later in life we attempt to repair early learning deficits in mathematics, the costlier the remediation becomes. [ABSTRACT FROM AUTHOR]

There is consensus in the international mathematics teacher education literature that teachers should, at the most basic level, have mastery of the content knowledge they are required to teach. In this paper we test this assumption empirically by analyzing the South African SACMEQ 2007 mathematics teacher test data which tested 401 grade 6 mathematics teachers from a nationally representative sample of primary schools. With items matched to curriculum grade bands, findings indicate that 79% of grade 6 mathematics teachers showed content knowledge levels below the grade 6/7 band, and that the few teachers with higher-level content knowledge are highly inequitably distributed. [ABSTRACT FROM AUTHOR]

This article describes the approach used to assess the performance of a Fourier transform infrared (FTIR) and principal component regression (PCR) chemometric method when measuring respirable quartz, kaolinite, and coal in samples from a variety of mines from different countries; relative to target assigned values determined using X-ray diffraction (XRD). For comparison, FTIR results using the partial least squares regression (PLSR) method are also available. Bulk dusts from 10 Australian mines were scanned using XRD and grouped into three sets based on the levels of quartz, kaolinite, and feldspar within their crystalline mineral composition. Prediction samples were generated from 5 of these Australian mine dusts, Durrans coal dust, 2 mine dusts from the UK, and a single South African mine dust (71 samples in total) by collecting the aerosolized respirable dust onto 25-mm diameter polyvinylchloride filters using the Safety in Mines Personal Dust Sampler (SIMPEDS) operating at 2.2 l min−1. The predicted values from the FTIR chemometric methods were compared with assigned target values determined using a direct on-aerosol filter XRD analysis method described in Method for the Determination of Hazardous Substances (MDHS) 101. Limits of detection (LOD) and uncertainty values for each analyte were calculated from a linear regression between target and predicted values. The uncertainty was determined using the calibration uncertainty equation for an unweighted regression. FTIR results from PCR and PLSR are very similar. For the PCR method, the LOD for quartz, kaolinite, and coal were 5, 25, and 71 µg, respectively. For quartz, an LOD of 5 µg corresponds to an airborne quartz concentration of 10 µg m−3, assuming a 4-h sampling time and collection flow rate of 2.2 l min−1. The FTIR measurement met the expected performance criteria outlined in ISO 20581 when sampling quartz for more than 4 h using a flow rate of 2.2 l min−1 at a concentration of 0.1 mg m−3 (100 µg m−3), the current workplace exposure limit in Great Britain. This method met the same performance criteria when measuring exposures at the Australian Workplace Exposure Standard (WES) concentration of 0.05 mg m−3, although in this case a sampling period greater than 8 h was needed. [ABSTRACT FROM AUTHOR]

Estimation equations based on different body segments are commonly used to predict height in patients whose height cannot be directly measured. This study aimed to assess the agreement between measured (reference) height and height predicted from published equations derived from measurement of body segments, in a South African public hospital setting. A descriptive cross-sectional study was undertaken. Medical, surgical, pulmonary, orthopaedic, cardiovascular and general wards at three public hospitals in Bloemfontein. Admitted patients, 20–50 years old; able to stand upright without assistance and without medical conditions or treatments affecting height. Stadiometer height, recumbent height, arm span, demi-span, ulna length, knee height, tibia length, fibula length and foot length were measured with standardised techniques. Height, predicted by 12 published equations, was compared with stadiometer height by 95% confidence intervals (CI) and Bland–Altman analysis. The median stadiometer height of the sample (n = 141; 38.3% female; median age 38.8 years, IQR 33.3–44.4 years) was 165.5 cm (males 169.3 cm; females 158.4 cm). Only a set of equations based on knee height and standardised on a large population of adults < 65 years in the United States estimated height without statistically significant deviance from the stadiometer height. Most standardised equations applied to hospitalised adults in a South African public health setting resulted in height estimations that differed significantly from height. Thus, equations standardised on other populations may not be suitable for the South African population, possibly due to differences in genetic and environmental factors. [ABSTRACT FROM AUTHOR]

This study, conducted in one high-achieving secondary school in a disadvantaged area in the Western Cape province of South Africa, asks whether mathematics teachers alter their "talk" across the face-to-face and computer-based lessons. Data were gathered through video recordings of teacher/student interactions across ten face-to-face and computer-based mathematics lessons conducted by two teachers. Findings indicate that the teachers studied significantly altered their "talk" across the two contexts, with a medium effect size. Further, a significant association at a medium effect level between any two of the three variables—location of lesson, "talk" type and scale of interaction—was found. In particular, teachers used significantly less mathematical talk in the computer lessons. As language is the primary mediator of conceptual acquisition (Vygotsky, 1978), this calls into question what mathematical concepts are learnt in a computer-based lesson. [ABSTRACT FROM AUTHOR]

This article draws on the notion of epistemic agency to illustrate how the enactment of shared epistemic agency is enabled or hindered in a mathematics classroom for student teachers. I used data from an ethnographic study that was conducted in a third-year class of mathematics for educators. Data was drawn from verbal interactions that took place between mathematics student teachers, and between student teachers and myself as their lecturer, as they worked on class tasks. A narrative mode of analysing data was employed to synthesise data from critical incidents, while excerpts of these incidents represented data. From this analysis, I argue that, with extended wait time by a facilitator, students' disposition of epistemic virtues and vices may enable or hinder enactment to epistemic agency, respectively. In article, those vices presented themselves as epistemic stinginess, prejudices against answers by peers and epistemic disclaimer. The epistemic virtues were presented as impartiality and intellectual courage. I further suggest that the recommended wait time of 1–3 during classroom questioning and answering should be extended for classes where epistemic practices are encouraged. [ABSTRACT FROM AUTHOR]